Buckling of columns with top and distributed loading using Rayleigh's method: assessment of two cases of boundary conditions

Resumo

The problem of buckling in compressed parts has been the subject of study by many researchers due to the importance that these structural elements have for different areas of engineering. The compressive capacity of columns can be quantified using the so-called critical buckling load. The first studies date back to the work of Euler and Greenhill that began in the 18th century. Other contributions have been made since then. One of the most relevant for this field of study is the Rayleigh solution formulated to understand the vibration of elastic systems, whose equations can be directly used in determining the critical buckling load. The central feature of this method is the possibility of associating continuous systems with an equivalent system with a single degree of freedom. The Rayleigh method is used to define the critical buckling load of two columns under the simultaneous action of concentrated and distributed load along their length. Prismatic section parts are evaluated considering two boundary conditions. The values suggested in the literature are compared to the current results.